Some Remarks on General Nonlinear Stochastic $H_{\infty }$ Control With State, Control, and Disturbance-Dependent Noise

This technical note studies the nonlinear stochastic H
_∞
control of Itô-type differential systems with all the state, control input and external disturbance-dependent noise ( (x,u,v)-dependent noise for short). A sufficient condition is given for the finite/infinite horizon H
_∞
control of such a system by means of an Hamilton-Jacobi inequality (HJI) instead of three coupled Hamilton-Jacobi equations (HJEs) as in previous literature.